of Edinburgh , Session 1871—72 
61 1 
Hen'ce 
i 
k' L 
_4 
k 
or 
J_ = 2 Jk 
k x 1 + k 
Lagrange’s transformation is equivalent to 
and we thus have 
whose application to the pendulum problem is obvious. 
5. On the Decomposition of Forces externally applied to an 
Elastic Solid. By W. J. Macquorn Bankine, C.E., 
' LL.D., F.B.SS. Bond, and Edin. 
The principles set forth in this paper, though now (with the 
exception of the first theorem) published for the first time, were 
communicated to the French Academy of Sciences fifteen yearn 
ago, in a memoir entitled “ de lEquilibre interieur d’un Corps 
solide, elastique, et homogene,” and marked with the motto, 
“ Obvia conspicimus, nubem pellente Mathesi,” the receipt of which 
is acknowledged in the Cornptes Bendus of the 6th April 185T 
(vol. xliv. p. 706.) 
The author quotes a theorem discovered by him, and previously 
published in the Philosophical Magazine for December 1855, 
called “ the Principle of Isorrhopic Axes,” viz., “ Every self- 
( Abstract .) 
